Question

The angle of elevation of a ladder leaning against a wall is 60° and the foot of the ladder is 9.5 m away from the wall. Find the length of the ladder.

Answer 1

Given: Angle of elevation of ladder = 60°, distance from foot of ladder to wall (adjacent) = 9.5 m.

Step-wise calculation:

1. Draw the right triangle:

Ladder = Hypotenuse (L)

Base = Adjacent = 9.5 m

Angle at foot = 60°

2. Use cosine:

cos 60° = `"Adjacent"/"Hypotenuse"`

= `9.5/L`

3. `cos 60^circ = 1/2`

So `1/2 = 9.5/L`.

4. Solve for L:

`L = 9.5 ÷ (1/2)` 

= 9.5 × 2

= 19 m

The length of the ladder is 19 m.